A system of the type defined above is known; it consists of an actual franking machine and an apparatus separate from the franking machine, comprising the weighing unit, a keyboard for entering tariff data and an electronic unit. This system does not guarantee that the franked item is the same as that which was previously weighed. Thus a system of this type presupposes that the franking procedure is carried out by postal administration staff. If the system is used by users, the administration will then have to subsequently check that the postal items processed by the system are correctly franked.